The invention relates to feeding systems for use in aircraft or hospitals, for example, which can heat a food dish while the dish is on a tray in a tray cart. More particularly, it relates to such a feeding system wherein a plurality of heater shelves, which are mounted in the cart, are adapted to be slidingly engaged by dishes which are passed over them while the trays pass under them and while the dishes are retained against movement relative to the trays. An example of such a feeding system is disclosed in Dodd et al., U.S. Pat. No. 4,346,756 which is assigned to a common assignee, and whose disclosure is incorporated by reference herein. In the Dodd et al. patent, the dishes to be heated are disclosed as having a pair of integral parallel runner portions. One of the runner portions is retained between a pair of parallel, vertically extending guide rib means on the tray which captures it both when the dish is on the tray and outside the cart or when it is in the cart and raised up by the heater. The other runner portion is adapted to contact the bottom of the tray when the tray is out of the cart. When the tray is in the cart, the said other runner portion rests on the top of a bracket which supports the heater shelf in a cantilever fashion from the wall of the cart. In order to minimize weight and space requirements and maximize the number of trays and meals which can be stored and heated in a single cart, the vertical extent of the runner portions has been kept relatively low, about 0.28 inches. In the usual operating situation, the existing dishes and trays have cooperated in their intended manner quite satisfactorily. However, when the cart containing the loaded trays is in transit from a commissary to an aircraft and the truck carrying it is subjected to rather violent bumps, it is sometimes possible for one dish runner to be lifted up from between the pair of guide ribs which guide it. In such a situation, the runner could also move longitudinally and land on top of one of the two transverse abutment means which normally engage the ends of the runner and restrain the dish in a fixed position over a heater shelf element. Thus, it would be possible for further jostling movement to cause the dish bottom to slide at least partially off the heater shelf, and thus out of the full surface engagement which is needed for rapid efficient heating. This is especially true since the other dish runner is free to slide over the bracket that supports the heater shelf. In such an instance, the dish would not get properly heated unless the cart was opened and visually inspected very carefully when it reached the aircraft to detect and correct any shifting of dishes. It would also be conceivably possible for a dish to jump out of its guide track if the tray on which it was positioned had become considerably warped after a number of heating and washing cycles.